## Mathematics

### Solving the problem.

Most schools start with rules and computations that almost never relate to daily life. At Pomfret, we start with real-world problems, and then learn the math so we can solve them. Incoming third formers must take three years of mathematics, through Integrated Math III/Honors Algebra II and through the junior year. Seniors must pass all yearlong courses and all courses in the spring term of the senior year in order to be considered for graduation.

- Pre-calculus
- Advanced Pre-calculus
- Honors Pre-calculus
- Calculus I
- Advanced Calculus I
- Advanced Calculus II
- Advanced Calculus III
- Advanced Calculus IV
- Advanced Statistics
- Economics and Entrepreneurship
- Financial Literacy
- Honors Algebra II
- Honors Geometry
- Integrated Mathematics I
- Integrated Mathematics II
- Integrated Mathematics III
- Macroeconomics
- Microeconomics
- Stats I: Descriptive
- Stats II: Probability
- Stats III: Inferential
- Advanced Topics in Mathematics

## Pre-calculus

#### OFFERED: yearlong

This in an intermediate course designed for students who have completed our Integrated Mathematics sequence and wish to strengthen their mathematical background. This course investigates linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. Additional topics covered include vectors, matrices, sequences and series, and conic sections. Emphasis is placed on mathematical modeling and problem solving. Prerequisite: Integrated Mathematics III or its equivalent.

## Advanced Pre-calculus

#### OFFERED: yearlong

This fast-paced course provides students with an in-depth investigation of linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. The pace and rigor of this course allows for a greater breadth and depth analysis of the material. Additional topics include vectors, parametric equations, polar coordinate system, and limits. This course provides the analytical foundation and framework for Advanced Calculus. Prerequisites: High achievement in Algebra II Honors or its equivalent.

## Honors Pre-calculus

#### OFFERED: yearlong

This course closely investigates the functions taught in Honors Algebra II. This course provides students with a more extensive examination of linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. Additional topics covered include vectors, matrices, sequences and series, and conic sections. Emphasis is placed on mathematical modeling and problem solving. Prerequisite: Algebra II Honors or high achievement in Integrated Mathematics III or its equivalent.

## Calculus I

## Advanced Calculus I

#### OFFERED: yearlong

This course will include limits and continuity; the Fundamental Theorem of Calculus; definition of the derivative of a function and techniques of differentiation; applications of the derivative to maximizing or minimizing a function; the chain rule, mean value theorem, and rate of change problems; curve sketching; definite and indefinite integration of algebraic, trigonometric, and transcendental functions, with an application to calculation of areas and volumes of revolution. Prerequisite: Honors Pre-calculus or its equivalent with approval by the Mathematics Department.

## Advanced Calculus II

#### OFFERED: yearlong

This second year Advanced Calculus course will include differentiation and integration of transcendental functions; parametric equations and polar coordinates; techniques of integration; sequences and series; improper integrals. Prerequisite: Advanced Calculus I or its equivalent with approval by the Mathematics Department.

## Advanced Calculus III

#### OFFERED: fall term

Advanced Calculus III covers topics in Differential Equations and Vector Calculus. Other topics might include Integration in Double and Triple Integrals. The course is designed to be a continuation of those topics covered from Advanced Calculus II. Prerequisite: Advanced Calculus II or with approval by the Mathematics Department

## Advanced Calculus IV

#### OFFERED: winter term

Advanced Calculus IV is a one term course which will focus on some advanced topics in Differential Equations and in Multi-variable Calculus. In particular, Laplace transforms will be explored along with their use in solving differential equations. Power series solutions will be explored. Other topics might include, Green's Theorem, Stokes's Theorem, the Divergence Theorem and Surface Integrals. Departmental approval required

## Advanced Statistics

#### OFFERED: yearlong

This course is equivalent to an introductory, non-calculus based college course in statistics. Since statistics is a key element of many courses of study in college, any student interested in psychology, sociology, humanities, business, economics, biology/life sciences, medicine, mathematics/statistics, engineering, etc. would benefit from this course. The purpose of the advanced placement course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploratory analysis, planning a study, probability, and statistical inference. Students must have their own graphing calculator, which has a full menu of statistical functions. Science, engineering, business, and mathematics majors usually take an upper division calculus based course in statistics, for which the Advanced Statistics course will be an effective preparation. Prerequisites: Integrated Mathematics III, strong mathematical background, and permission from the instructor.

## Economics and Entrepreneurship

#### OFFERED: spring term

In this course, students will learn about starting and managing a small business. Readings, viewings of the show “Shark Tank,” and class discussion will guide our learning. Students will complete numerous “practice pitches” where they have a short window of time to pitch an idea to an audience of stakeholders while also considering a variety of marketing strategies. Inquiries into local businesses and learning from successful Pomfret alumni will be interspersed throughout the course. By the end of the term, students will develop their own ideas for a business and write a detailed business plan. This course is open to juniors and seniors or by departmental approval.

## Financial Literacy

#### OFFERED: spring term

The Financial Literacy course is designed to inform and educate students in concepts of personal finance and money management. Students will begin to develop the skills and strategies that promote responsible personal financial planning. Topics include financial psychology; loans and credit; budgeting; savings and investing in the capital markets. This course is open to seniors or by department approval.

## Honors Algebra II

#### OFFERED: yearlong

Topics covered in this course are similar to those found in the regular section of Algebra II, but the pace and academic rigor allows for the greater breadth and depth analysis of material. Additional topics include exponential and logarithmic functions, right angle triangle trigonometry, circular functions, sequence and series, and might include elementary probability and statistics. Prerequisites: High achievement in both Integrated Mathematics I and II

## Honors Geometry

#### OFFERED: yearlong

Topics covered in this course are similar to those that are found in a regular section of Geometry, but the pace and academic rigor allows for the greater breadth and depth analysis of material. This course is for students possessing a strong understanding of Algebra I concepts, high mathematical aptitude, and good reasoning skills. Prerequisite: High achievement in Integrated Mathematics I

## Integrated Mathematics I

#### OFFERED: yearlong

The Integrated Mathematics Sequence provides an alternative to Algebra I, Geometry, and Algebra II. The courses spiral concepts from algebra and geometry while continuing the development of fundamental skills. Integrated Mathematics I focuses algebra, linear and exponential functions, sequences, systems of equations, descriptive statistics, and introductory geometry. The course builds upon the foundations of arithmetic and develops the basic concepts of algebra. It strives to present algebra as a natural and yet necessary extension of arithmetic. The emphasis is on solving problems in context rather from drill and practice for its own sake. Successful completion of this course provides a firm foundation in algebra and the tools needed to proceed through the Integrated Mathematics Sequence.

## Integrated Mathematics II

#### OFFERED: yearlong

The Integrated Mathematics Sequence provides an alternative to Algebra I, Geometry, and Algebra II. The courses spiral concepts from algebra and geometry while continuing the development of fundamental skills. Integrated Mathematics II focuses on quadratic functions, probability, advanced geometry, and introductory trigonometry. This integrated program incorporates content not only from algebra but also from numbers and operations, geometry, proportional reasoning, data interpretation, and probability and statistics. The emphasis is on developing and strengthening algebraic thinking, conceptual understanding, and basic skills. The course stresses symbolic, graphing, and tabular representations of information and data. Integrated Mathematics II is the second of three courses in our Integrated Sequence.

## Integrated Mathematics III

#### OFFERED: yearlong

The Integrated Mathematics Sequence provides an alternative to Algebra I, Geometry, and Algebra II. The courses spiral concepts from algebra and geometry while continuing the development of fundamental skills. Integrated Mathematics III focuses on extending algebra and functions (including radicals, rational expressions, polynomial functions, logarithmic functions, sequences and series), trigonometry, and probability. This is the final year of a program that spirals concepts from Algebra, Geometry, and Statistics over a three-year period while continuing the development of problem solving strategies. This course places an emphasis on functions and geometry concepts taught in previous courses with a focus on the geometry of triangles and transforming graphs. Upon completion of the program, students are evaluated for placement in their math courses for the following year.

## Macroeconomics

#### OFFERED: winter term

In this course, students will begin exploring how a nation’s income is measured, carefully analyze Gross Domestic Product and debate whether it’s an outdated measurement for growth. Next, a look into costs of living will segway into inflation and its relationship with unemployment. Understanding measurements for savings and investment will guide students into a look at the basic tools of finance. Open-economy concepts of trade balance, exchange rate, and aggregate supply/demand will broaden the lens of the class and initiate a look into developing nations and their economies. Lastly, students will play a stock game that will allow them to buy and short sell stocks on an on-line platform, tracking their portfolio over the course of the term. Short writing assignments, quizzes, and tests will be the primary forms of assessment in this class.

This courses is open to juniors and seniors or by departmental approval.

## Microeconomics

#### OFFERED: fall term

Building off ten key principles of economics (Principle # 4: People respond to incentives), students will delve into the market forces of supply and demand, elasticity, government intervention, and study a variety of market models from competitive to monopolistic. The course will also ask students to critically explore: costs of production, equilibrium in the labor market, earnings and discrimination, and income inequality. A big fundamental question to this course as well as the Macroeconomics elective will be: What is growth and how is it measured? Students will be asked to consider their own personal values as a consumer, as well as those behind the businesses they purchase goods and service from. Discussion and structured debates will be the primary format for this class. This course is open to juniors and seniors or by departmental approval.

## Stats I: Descriptive

#### OFFERED: fall term

Statistics I: Descriptive Statistics covers the basic principles of one-variable topics including graphical representations of data, measures of central tendency, and measures of variability. Two-variable data analysis is based on linear regression and correlation. This course will also introduce sampling and experimentation: planning and conducting a study, including sample surveys, observational studies, and experiments. Descriptive statistics are distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aim to summarize a data set, rather than use the data to learn about the population that the data are thought to represent.

## Stats II: Probability

#### OFFERED: winter term

Stats II: Probability and Probability Distributions introduces probability spaces, expectation values, and conditional expectations. It develops the basic tools of probability theory, such fundamental results as the weak and strong laws of large numbers, and the central limit theorem. This course covers the basic principles of the theories of probability and its applications. Topics include combinatorial analysis used in computing probabilities, the axioms of probability, conditional probability and independence of events; discrete and continuous random variables; binomial, geometric, univariate, and bivariate normal distributions. Prerequisite: Stats I or departmental permission

## Stats III: Inferential

#### OFFERED: spring term

In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. More substantially, the terms statistical inference, statistical induction, and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from datasets arising from systems affected by random variation. Prereq: Stats I and II or departmental permission

## Advanced Topics in Mathematics

#### Offered: Spring Term

The Advanced Topics in Mathematics course will include topics from Differential Equations and Multivariable Calculus that were not explored in previous courses. Some study of Archimedes' proofs and their relation to calculus will also be explored. This advanced topics course is an extension of the Adv. Calculus III and IV series offered in prior terms.